Batch triangulating a model made of multiple objects
separate objects can be edited one at a time, that is what you are doing now.
if you wish to edit all object at once, you can try to join them (ctrl-j) and then go into edit mode. so:


select all objects you wish to edit at once (it works only with objects of the same type, eg: meshes and curves can't be joined, without conversion, which probably you don't want to do...)
press ctrl-j
you have a single object now, composed of all the vertices, edges, faces jou had before. They are now together in the same object but still not connected yo those previously belonging to other objects


Now you can edit the object at once.

When finished, if you have to separate different objects back, you can:


select the joined object
go to edit mode
deselect everything (A key)
select only 1 vertex, from one mesh once belonging to a separate object
select linked vertices, with L key
separate selected vertices in a separate object, with P key
repeat until done